Geometric approach to quantum theory and inclusive scattering matrix

I give a formulation of quantum theory where the starting point is a convex set of states. I show that
the formulas for probabilities can be derived from first principles.  One can define particles as
elementary excitations of ground state and quasiparticles as elementary excitations of translation invariant stationary state. The collisions of (quasi)particles  in the geometric approach are described by  inclusive scattering matrix.  (Inclusive cross-sections can be expressed in terms of inclusive scattering matrix. Only
inclusive cross sections make sense for collisions of quasiparticles.)